Method and apparatus for correcting excess signals in an imaging system

ABSTRACT

A method and apparatus for excess signal compensation in an imaging system is described. In one particular embodiment, the invention provides for non-linear background, offset (due to time dependent dark current) and/or lag (including constant, linear and non-linear terms, due to image persistence) corrections of large area, flat panel imaging sensors.

RELATED APPLICATION

This application is a continuation of U.S. patent application Ser. No.11/729,611 filed Mar. 29, 2007 now U.S. Pat. No. 7,423,253 which is acontinuation of U.S. patent application Ser. No. 10/688,484 filed Oct.16, 2003 now U.S. Pat. No. 7,208,717 which claims the benefit of U.S.Provisional Patent Application No. 60/419,132, filed Oct. 16, 2002.

TECHNICAL FIELD

This invention relates generally to large area, flat panel imagers. Morespecifically, the invention relates to amorphous silicon and/or organicsemiconductor thin-film-transistor (TFT) or diode-switched arrayimagers.

BACKGROUND

Large area flat panel imagers function by accumulating charge oncapacitors generated by pixels of p-i-n photodiodes (amorphous siliconor organic semiconductor) with scintillators or by pixels ofphotoconductors. Typically, many pixels are arranged over a surface ofthe imager where TFTs (or single and/or double diodes) at each pixelconnect the charged capacitor to a read out amplifier at the appropriatetime. A pixel is composed of the scintillator/photodiode/capacitor/TFTor switching-diode combination or by the photoconductor/capacitor/TFT orswitching-diode combination. Often the photodiode intrinsically hasenough capacitance that no separate charge storage capacitor isrequired. As illustrated in FIG. 1A, radiation (e.g., alpha, beta,gamma, X-ray, neutrons, protons, heavy ions, etc.) strikes thescintillator and causes the scintillator to generate visible light. Thevisible light strikes a photodiode and generates an electric current.Alternatively, an imager may be configured such that the radiationstrikes a biased photoconductor to generate the electric current, asillustrated in FIG. 1B. The current charges a capacitor (where theillustrated capacitor includes the self capacitance of thephotoconductor) and leaves a charge on the capacitor. The integratedcharge on the capacitor is proportional to the integrated lightintensity striking the respective photoconductor for a given integrationtime. At an appropriate time, a switch (e.g., a TFT or switchingdiode(s)) activates and reads out the charge from the capacitor onto acharge sensitive amplifier (not shown).

For long integration times, typically over 20 seconds for amorphoussilicon technology, there is a linear increase in charge Q_(Li) to thecapacitor charge (in coulombs) of pixel “i,” as a function of discreteframe time T, due to a constant leakage (or dark) current from theswitch (e.g., TFT), diode or photodetector. This dark current I_(D) ison the order of 1-2 femtoamps (fA) for 100 to 200 micron wide pixels ofamorphous silicon TFT construction. The expression for Q_(Li) is thedark current I_(D) multiplied by T. Dark current I_(D) may be constantor time varying; giving an excess charge Q_(E) contribution that iseither linear or non-linear with respect to time, respectively. Thislinear dark charge contribution to Q_(Li) is subtracted from the totalcharge Q_(Ti) read off the capacitor of pixel “i” in order to providethe true image charge Q_(Si). Subtracting the dark-current chargecontribution (either linear or non linear), from the total charge Q_(Ti)read off the capacitor, is called background (or offset) correction.

In addition to dark current charge contributions from the switch (e.g.,TFT) there are leakage (or dark) current charge contributions from thecapacitor and the photodiode. The true image charge Q_(Si) is obtainedby subtracting the background (or offset) dark charge contributions fromthe measured charge Q_(Ti) of pixel “i.” The simplest backgroundcorrection method is to subtract a constant fraction of the charge thatwas present on pixel “i” during at least one, and sometimes additional,prior frames.

Prior background correction methods have been implemented to estimateoffset correction. One prior background correction method discussed inU.S. Pat. No. 5,452,338, isolates the offset image by acquiring an imagewhen the detector is not exposed to X-rays, using the same timing usedin acquiring the X-ray exposed images. The image acquired after exposureis then subtracted from future frames. One problem with the use of onesingle frame in determining the offset correction is the offset imageintroduces additional noise. To reduce the additional noise, multiplenon-exposed images may be acquired and then averaged. One problem usinga single image or an average of multiple images is the offset signalsmay drift with time, temperature, and other extrinsic factors while thesingle image or averaged image remains constant.

Another prior background correction method discussed in a paper bySussan Pourjavid, et al., entitled “Compensation for Image Retention inan Amorphous Silicon Detector” (SPIE Conference on Physics of MedialImaging, February 1999), and U.S. Pat. No. 5,452,338, continuouslyupdates the offset images to compensate for drift in the offset signals.The method, described in the above references, models the time responseof the background contribution from leakage current (or dark image) inthe diodes as a linear time invariant system (LTI) using linear systemstheory (least square method). The LTI system derived from the responsemodel is then used to predict the offset needed for image correction.However, in modern medical imaging equipment, for example, there is ademand for real-time, 30 frames per second images, where scans are madewith 33 millisecond integration times. Even more advanced imagingapplications, like computed tomography, can use even higher frames ratesof 120, 360 or even 900 frames per second, corresponding to respectiveintegration times of 8, 3 and 1 milliseconds, respectively. Backgroundcorrection using least square prediction of discrete frame time in suchsituations is not as effective. With near real-time imaging, for example3 frames per second (FPS) or faster, background correction with leastsquare prediction can introduce significant image errors and artifacts.A more effective method for background (or offset) correction is neededin short-integration-time imaging applications.

SUMMARY OF AN EMBODIMENT OF THE INVENTION

The present invention pertains to a method and apparatus for excesscharge corrections in flat panel imaging sensors.

Additional features and advantages of the present invention will beapparent from the accompanying drawings, and from the detaileddescription that follows below.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention is illustrated by way of example and not intendedto be limited by the figures of the accompanying drawings.

FIG. 1A is an illustration of conventional components of an imagersensor array.

FIG. 1B illustrates an alternative configuration of an imager sensorarray.

FIG. 2A illustrates one embodiment of an imaging system.

FIG. 2B illustrates one embodiment of an imager sensor array.

FIG. 2C illustrates another embodiment of an imager sensor array.

FIG. 3 illustrates one example of a graph of excess current generated byboth a constant and time varying excess current components.

FIG. 4 is one expression for a time varying excess current I_(E) and itsintegration with time to determine an excess charge Q_(E) that isnon-linear in time.

FIG. 5 illustrates one example of a graph showing time varying excess orleakage current for multiple TFTs connected in parallel.

FIG. 6 illustrates a table correlating frame rate with integration time.

FIG. 7 is a flow diagram illustrating one embodiment of a method ofestimating the excess signal and compensating for the excess signal inan imaging system.

FIG. 8 is a flow diagram illustrating one embodiment of a method ofestimating the excess signal using one reference image frame, andcompensating for the excess signal in an imaging system.

FIG. 9 is a flow diagram illustrating one embodiment of a method ofestimating the excess signal using two reference image frames, andcompensating for the excess signal in an imaging system.

FIG. 10A illustrates an exemplary fluoroscopic image frame afterradiographic exposure without compensation for the excess signal.

FIG. 10B illustrates an exemplary fluoroscopic image frame afterradiographic exposure with compensation for the excess signal.

FIG. 11A illustrates an exemplary fluoroscopic image frame of a pelvisphantom after radiographic exposure without compensation for the excesssignal.

FIG. 11B illustrates an exemplary fluoroscopic image frame of a pelvisphantom after radiographic exposure with compensation for the excesssignal.

FIG. 12 illustrates one example of a graph showing measured signallevels in an imaging system as a function of time.

FIG. 13 illustrates another example of a graph showing measured signallevels in an imaging system as a function of time.

FIG. 14 illustrates another example of a graph showing the measuredsignal levels in an imaging system as a function of time.

FIG. 15 illustrates one example of a look-up table.

FIG. 16A illustrates one example of a graph showing the remaining excesssignal after compensation using different estimation methods.

FIG. 16B illustrates one example of a graph showing the remaining excesssignal after compensation of two estimation methods at a smaller scalethan FIG. 16A.

DETAILED DESCRIPTION

In the following description, numerous specific details such as specificmaterials, processing parameters, processing steps, etc., are set forthin order to provide a thorough understanding of the invention. Oneskilled in the art will recognize that these details need not bespecifically adhered to in order to practice the claimed invention. Inother instances, well known processing steps, materials, etc., are notset forth in order not to obscure the invention.

Some portions of the description that follow are presented in terms ofalgorithms and symbolic representations of operations on data bits thatmay be stored within a memory and operated on by a processor. Thesealgorithmic descriptions and representations are the means used by thoseskilled in the art to effectively convey their work. An algorithm isgenerally conceived to be a self-consistent sequence of acts leading toa desired result. The acts are those requiring manipulation ofquantities. Usually, though not necessarily, these quantities take theform of electrical or magnetic signals capable of being stored,transferred, combined, compared, and otherwise manipulated. It has beenproven convenient at times, principally for reasons of common usage, torefer to these signals as bits, values, elements, symbols, characters,terms, numbers, parameters, or the like. The term “coupled” as usedherein means coupled directly to, or indirectly through one or moreintervening components. References to charge may be expressed in termsof current integrated over time. Current is the amount of electriccharge flowing past a specified circuit point per unit time.

The invention provides a method and apparatus for correction of imageartifacts in imaging sensors due to excess charge. Sources of excesscharge may be contributed by, for examples, leakage currents, offset(due to time dependent dark current), and lag currents (includingconstant, linear and non-linear terms, due to image persistence). Thedark current charge contributions may be introduced from the switch(e.g., TFT). The leakage (or dark) charge contributions may beintroduced from the capacitor and the photodiode. There may bepersistent or “lag” charge contributions (and pixel capacitor chargecontributions) from the photoconductor/photodiode or from incompletecharge read out from the capacitor, in a given frame of prior framessubjected to high dose radiation exposure. This “lag” chargecontribution can be either linear or non linear in a discrete frame timeT. Lag charge contributions are particularly prevalent when one frame isbright and the next is dark.

For purposes of the discussion hereafter, the term signal refers to thedigital output of an imager, for example, as may be generated at theoutput of A/D converters 17 discussed below in relation to FIG. 2A. Thedigital signal (e.g., S_(E) 235) is generally proportional to themeasured charged (e.g., Q_(E) 35) on the output of the imager sensorarray 16, as is known in the art.

In one embodiment, the method includes determining an integration timebased on the frame rate of the images and calculating a non-linearbackground signal S_(NLi) and/or prior-frames-dependent lag signalS_(LAGi) per pixel “i.” The lag signal S_(LAGi) may be a constantfraction of the true image signal S_(Si) of pixel “i,” or a constantfraction of the measured signal S_(Ti) of pixel “i,” from one or moreprior frames with appropriate weighting factors. In order to correctimages, the method may include subtracting the lag signal S_(LAGi) andthe non-linear background signal S_(NLi) from the measured signal S_(Ti)representative of the charge on the capacitor of each pixel “i” for eachimage frame.

For faster than 0.1 frames per second, one method of generating the trueimage signal S_(Si) of pixel “i,” is to estimate the modeled (ortheoretical or simulated), time-dependent, excess (e.g., leakage, dark,and lag) charge as a function of time from zero to an integration time.Another method of calculating true image signal S_(Si) is to integrate asmooth curve fit of experimental data of the time dependent excesscharge as a function of time. One value for the integration time is thereciprocal of the frame rate. The estimated excess current is composedof the non-linear background signal S_(NLi) and/or of the calculated lagsignal S_(LAGi) is subtracted from a measured signal S_(Ti) of a pixel“i” in order to produce the true image signal S_(Si) of pixel “i,”typically with frame rates faster than 0.1 frames per second.

In one embodiment, the method includes estimating the excess signalS_(E) (representative of the excess charge Q_(E)) by using a referenceimage frame when the end of exposure time of a high-dose radiographicimage is known. The method determines the difference between the frametime of the reference image frame and the end of exposure time of thehigh-dose radiographic image. In one embodiment, the excess signal maybe estimated using a power function. The power function uses themeasured signal S_(T) (representative of a measured charge) of thereference image frame and the difference in time between the frame timeof the reference image frame and the end of exposure time to determine acoefficient. The coefficient is then multiplied by a time-varyingalgebraic decay to estimate the excess signal S_(E). The excess signalS_(E) is the integral of the excess signal over the frame time. Inanother embodiment, the excess signal may be estimated using a look-uptable. One example of using a look-up table may include indexing apre-calculated excess signal S_(PRE) to estimate the excess signal S_(E)(representative of the excess charge Q_(E)) using a post exposure numberof frames and measured signal S_(T) of the reference image frame. Thedifference in time is then converted to a frame number based on theframe rate. Once the excess signal S_(E) has been estimated using atleast one of the power function and the look up table, the method mayinclude subtracting the estimated excess signal S_(E) from the measuredsignal S_(T) for an image frame. Subtracting the estimated excess signalS_(E) of the image frame may remove significant image errors andartifacts that may appear in the present frame as “ghost images” fromradiation incidents during one or more prior frames.

In another embodiment, the method includes estimating the excess signalS_(E) by using two reference image frames at two different frame times.Two reference image frames may be selected when the end of exposure timeof a high-dose radiographic image is unknown. The two frame times of thetwo reference image frames may be based on the frame rate, and may berepresented as frame numbers of the selected reference image frames. Themethod determines the difference in time between the two frame times andthe frame time of the image selected for compensation. In oneembodiment, estimating the excess signal S_(E) may be done using a powerfunction. The power function uses the total measured signal S_(T) of atleast one of the two reference image frames and the difference in timebetween the two reference image frames to determine a coefficient. Thecoefficient is then multiplied by a time-varying algebraic decay toestimate the excess signal S_(E). In another embodiment, the excesssignal S_(E) may be estimated using a look-up table. One example ofusing a look-up table may include indexing a pre-calculated excesssignal S_(PRE) to estimate the excess signal S_(E) using the framenumber and measured signal S_(T) of at least one of the two referenceimage frames. It should be noted that, in this embodiment, the framenumber is determined using the difference in time between the frametimes of the two reference image frames. The difference in time is thenconverted to a frame number based on the frame rate. In anotherembodiment, the excess signal S_(E) may be estimated using a recursivefunction. One example of using a recursive function to estimate theexcess signal S_(E) includes using the measured signal S_(T) of at leastone of the two reference image frames selected and the difference intime between the two frame times of the two reference image frames todetermine a previous frame coefficient. The previous frame coefficientis then used to determine a next frame coefficient. The next framecoefficient is then multiplied by the measured signal S_(T) of thereference image frame to estimate the excess signal S_(E) of the nextframe. Once the estimation of excess signal S_(E), has been determinedusing either the power function, and/or the look up table, and/or therecursive function, the method may include subtracting the estimatedexcess signal S_(E) from the measured signal S_(T) of an image frame.Subtracting the total excess signal S_(E) on an image frame may removesignificant image errors and artifacts that may appear in the presentframe as “ghost images” from radiation incidents during one or moreprior frames, such as frames of high-dose radiographic exposure.

FIG. 2A illustrates one embodiment of an imaging system. Imaging system2 includes a computing device 4 coupled to an imager sensor array 16.Imager sensor array 16 may be, for example, an amorphous silicon organicsemiconductor TFT or diode-switched array imager. As previouslydiscussed in relation to FIGS. 1A and 1B, imager sensor array 16functions by accumulating charge on capacitors generated by pixels ofp-i-n photodiodes (amorphous silicon or organic semiconductor) withscintillators or by pixels of biased photoconductors. Typically, manypixels are arranged over a surface of imager sensor array 16 where, forexample, TFTs (or single and/or double diodes) at each pixel connect acharged capacitor to charge sensitive amplifier 19 at the appropriatetime. Charge sensitive amplifiers 19 drive analog to digital (A/D)converter 17 that, in turn, converts the analog signals received fromamplifiers 19 into digital signals (e.g., S_(T), S_(E)) for processingby computing device 4. A/D converter 17 may be coupled to computingdevice 4 using, for example, I/O device 10 or interconnect 14. A/Dconverter 17 and charge sensitive amplifiers 19 may reside withincomputing device 4 or imager sensor array 16 or external to eitherdevice.

Computing device 4 implements the methods for correction of imagingsensors due to excess signal S_(E) representative of the excess chargeQ_(E) discussed herein. The methods that may be performed by computingdevice 4 constitute computer programs made up of computer-executableinstructions illustrated as steps in the following examples of themethods illustrated in the following figures. In one embodiment,computing device 4 includes a processor 6, storage device 8,input/output (IO) device 10, and memory 12 that are all coupled togetherwith interconnect 14, such as a bus or other data path. In anotherembodiment, the computing device may be implemented using ProgrammableLogic Devices (PLD) or Field Programmable Gate Arrays (FPGA), in whichthe mathematical operations are performed by physical devices likeadders, multipliers, etc. In another embodiment, the computing devicemay be implemented using specialized integrated circuits for dataprocessing like adders, multipliers, bus switches, registers, RAM, ROMlogic gates, etc.

Processor 6 represents a central processing unit of any type ofarchitecture (e.g., Intel architecture or Sun Microsystemsarchitecture), or hybrid architecture. In addition, processor 6 could beimplemented in one or more semiconductor chips. Storage device 8represents one or more mechanisms for storing data and/or instructionssuch as the method steps of the invention. Storage device 8 representsread-only memory (ROM), random access memory (RAM), magnetic diskstorage media, optical storage media, flash memory devices, and/or othermachine-readable media. Interconnect 14 represents one or more buses(e.g., accelerated graphics port bus, peripheral component interconnectbus, industry standard architecture bus, X-Bus, video electronicsstandards association related buses, etc.) and bridges (also termed buscontrollers). I/O device 10 represents any of a set of conventionalcomputer input and/or output devices including, for example, a keyboard,mouse, trackball or other pointing device, serial or parallel inputdevice, display monitor, plasma screen, or similar conventional computerI/O devices. Memory 12 represents a high-speed memory device forretaining data and processor instructions for processor 6 according tothe method steps of the invention. Memory 12 can be implemented usingany of the memory devices described above for storage device 8. Inaddition, memory 12 can be used as a data cache for processor 6. Whilethis embodiment is described in relation to a single processor computersystem, in another embodiment, the invention may be implemented in amulti-processor computer system.

FIG. 2B illustrates one embodiment of the sensor array components of animager. Imager sensor array 16 includes a bias voltage 27, aphotoconductor 26, capacitor 28, and switch 32. Radiation 24 (X-rays,alpha, beta and gamma particles, neutrons etc.) has various energiesdepending on the particular embodiment of imager sensor array 16. Inanother embodiment the imager sensor array 16, illustrated in FIG. 2C,comprises a photodiode 26 a receives visible light 25 from ascintillator 26 b. The scintillator 26 b receives radiation 24 (e.g.,alpha, beta, gamma, X-ray, neutron, proton, etc.) and generates visiblelight 25. Visible light 25 strikes photodiode 26 a and generates anelectric current I 29.

In an alternative embodiment, imager sensor array 16 may have otherconfigurations. For example, photoconductor 26 of FIG. 2B may be aphototransistor that directly receives radiation 24. In such anembodiment, the radiation 24 striking the biased phototransistorgenerates the electric current I 29.

The electric current I 29 charges capacitor 28 and leaves a charge valueon capacitor 28, where the integrated charge on capacitor 28 isproportional to the integrated light intensity striking photoconductor26 for a given integration time. Capacitor 28 is coupled to switch 32(e.g., a TFT or switching diodes). At an appropriate time, the controlinput 30 (e.g., gate of a TFT) activates switch 32 and reads out thecharge on capacitor 28 at node 34. The measured electric charge Q_(T) 36at node 34 may include the excess charge Q_(E) 35.

One source of excess charge Q_(E) 35 is switch 32. The operation ofswitch 32 is discussed below in relation to a TFT for ease of discussionpurposes only. In another embodiment other types of switching devicesmay be used, for example, switching diodes, and may also be sources ofexcess charge Q_(E) 35. When the charge value on capacitor 28 is read atnode 34 there may be leakage current from gate 30 that contributes tothe detected measured charge Q_(T) 36 at node 34. Other sources ofexcess charge Q_(E) 35 may be capacitor 28 and photoconductor 26. Lagfrom photoconductor 26 (or from photodiode 26 a) arises from chargeremaining in the present frame generated by radiation incident duringone or more prior frames, resulting in a “ghost image” of these earlierframes. In addition, lag arises from incomplete discharge of thecapacitor 28 due to insufficiencies like too few RC time constantsduring readout to completely discharge capacitor 28. If the lag sourceis persistent photocurrent from the photoconductor 26, one method tocompensate for lag charge in a current pixel may be to subtract afraction of the true image signal S_(i) of one or more prior frames fromthe true image signal S_(i) of the current pixel. If the lag source is aresult of incomplete readout discharge of the capacitor 28, one methodto compensate for the excess charge 35, may be to subtract a fraction ofthe measured signal S_(Ti) from one or more prior frames. Imagecorrection for the excess signal S_(E) (representative excess chargeQ_(E) 35) composed of non-linear background signal S_(NLi) and/or lagsignal S_(LAGi) may be increasingly helpful at imaging rates above 0.1frames per second. Excess signal S_(E) may arise from other componentsthat may be coupled to capacitor 28. Subtracting the excess signal S_(E)235 from the measured charge S_(Ti) 236 provides the true image signalS_(Si) 239 of an image of FIG. 2A.

FIG. 3 illustrates one example of a graph from an amorphous siliconsensor showing measured capacitor charge (in femtocoulombs or fC), fromexcess current, estimated with a constant current component varyinglinearly with time, and estimated time varying current varyingnon-linearly with time. The horizontal axis of graph 300 shows time inseconds while the vertical axis shows capacitor charge in fC. Measuredcharge is the charge accumulated on the capacitor during the integrationtime (frame time), typically 30 milliseconds to 1000 milliseconds.

Measured charge 310 through the TFT of FIG. 1 is measured, in oneexample, by enabling the TFT (putting it in a low impedance state) for ashort time (e.g., 5 to 200 microseconds) and transferring the chargeaccumulated on the sensor capacitor to a charge integration amplifier.Estimated constant measured charge with time, caused by the constantcurrent 320, provides accurate estimation with image acquisition timesgreater than 20 seconds, as shown in graph 300. At image acquisitiontimes below 20 seconds, the non-linear contribution Q_(Nli), caused bythe non-linear current, has an increased effect on pixel “i” chargecorrection.

One modeled expression for non-linear charge correction Q_(NLi) 330 isshown in FIG. 4. I_(E)(t) is one expression for current varyinginversely with time, where K is a constant and t is the time in seconds.The integration time T_(i) is determined by dividing one by the framerate, shown in FIG. 6. One value for K is described below with FIG. 5.Q_(NLi) is one expression for the excess (offset, background, or dark)charge Q_(E) 35 of the measured charge Q_(Ti) 36 for pixel “i” at node34, and is calculated by integrating the excess current I_(E)(t) overthe frame period (integration time). One skilled in the art willrecognize that I_(E)(t) modeling is only one method for adjusting fortime varying current. In an alternate embodiment, I_(E)(t) may beestimated by using other methods, for example a continuous smooth curvefit. In yet another embodiment, for example, I_(E)(t) is estimated by atheoretical model expression.

FIG. 5 illustrates one example of graph 500 showing current on thevertical axis and time on the horizontal axis, for multiple TFTsconnected in parallel. In one embodiment, K may be determined by placing1000 TFTs in parallel and measuring the current with time varying from0.0001 to 10 seconds. On graph 500, using a logarithmic scale for thetime, the result is estimated as a straight line with a negative slopeof ˜T⁻¹. Dividing by the 1000 TFTs results in 10⁻¹⁵ A (amp), which isone value for constant K. One skilled in the art will recognize thatother methods of determining a value for K may be used. In oneembodiment, for example, K is derived from theoretical values for TFTs.In another embodiment, K may be derived from measuring excess currentfrom a system in which the invention is to be practiced.

Additional ways of modeling the time varying excess current may include:I _(E)(t)=A·t ^(n)  (1)

In equation (1), n may be greater or less than zero but not equal tozero or one. The constant A may either be determined theoretically or bycomparison with measured data. Some typical n values are, for examples,−0.3, −0.5, −1.0 and −1.3.

$\begin{matrix}{{I_{E}(t)} = {\sum\limits_{i = {- m}}^{n}{B_{i}{\mathbb{e}}^{D_{i}t}}}} & (2)\end{matrix}$

In equation (2), B_(i) and D_(i) may be constants and m and n may beintegers. B_(i), D_(i), m, and n, may be determined either theoreticallyor by comparison with measured data.

$\begin{matrix}{{I_{E}(t)} = {\sum\limits_{i = {- m}}^{n}{F_{i} \cdot t^{i}}}} & (3)\end{matrix}$

In equation (3), F_(i) may be constant and m and n may be integers.F_(i), m, and n, may be determined either theoretically or by comparisonwith measured data.

$\begin{matrix}{{I_{E}(t)} = {\sum\limits_{i = {- n}}^{n}{G_{n}{\mathbb{e}}^{{\mathbb{i}}\; n\;\pi\;{T/1}}}}} & (4)\end{matrix}$

In equation (4), G_(n), equals ½ T times the integral (from −T_(i) to+T_(i)) of I_(E)(x)e^(−inπx/T) with respect to x, and T_(i) is theintegration time interval of interest and n is an integer large enoughfor the calculated I_(E)(T_(i)) value to approximate the observed valueto the desired precision.

FIG. 6 illustrates a table correlating frame rate with integration time.Integration time (T_(i)) is 1 divided by the frame rate. For example, aframe rate of 0.1 frames per second (FPS) yields an integration time of10 seconds, a frame rate of 1 FPS yields an integration time of 1second, a frame rate of 30 FPS yields an integration time of 0.033seconds, and a frame rate of 100 FPS yields an integration time of 0.01seconds.

FIG. 7 is a flow diagram illustrating one embodiment of a method ofestimating the excess signal S_(E) 235 output from A/D converters 19(representative of Q_(E) 35 in a pixel of a frame captured by the imagersensor array 16), and compensating for the excess signal S_(E) in thepixel of the captured frame. It should be noted that the methoddescribed herein may be implemented by the computing device 4 togenerate the excess signal S_(E) 235. The integration time is determinedbased on the frame rate, step 700. As demonstrated with FIG. 6,integration time is the reciprocal of the frame rate. One skilled in theart will recognize that integration time is also used for methods otherthan integration.

The method determines a value for K as discussed, for example, above inrelation to FIG. 5, step 710. In step 720, an estimation of the excesssignal S_(E) 235 composed of linear and non-linear background signalS_(NL), and/or non-linear lag signal S_(LAG), based on the constant (K)value and the frame rate, is calculated. In one embodiment, the excesssignal S_(E) 35 may be calculated, for example, by integrating I_(E)(t),with the determined value of K, over the integration time (T) (thereciprocal of the frame rate), as described above with respect to FIG.4. In another embodiment, the excess signal S_(E) 235 may be calculatedby summing I_(E)(t) over a series of steps. In step 730, the estimationof excess signal S_(E) 235 is subtracted from a measured signal S_(T)236. The measured signal S_(T) 236 is, for example, representative ofthe measured charge Q_(T) 36 read out of a node 34 of FIG. 2B at anappropriate time and contains contributions from the charge stored oncapacitor 28, also in FIG. 2B, as well as non-linear chargecontributions (excess charge 35) from TFT 32 if the frame rate is below20 seconds per frame, see FIG. 1. The result from step 730 includes anestimation of the excess signal S_(E) 235 arising from radiationincident on photodiode 26 a from one or more prior frames thatconstitutes a lag contribution. In an alternative embodiment, theprocessor 6 may use a look-up table storing excess signal S_(E) 235estimates versus integrated time values based on frame rates.

FIG. 8 is a flow diagram illustrating one embodiment of a method ofestimating the excess signal S_(E) 235 from a pixel of a frame capturedby the imager sensor array 16 using one reference image frame, andcompensating for the excess signal S_(E) 235 from the pixel of thecaptured frame. Each pixel of the reference image frame has a measuredsignal S_(T) 236. The excess signal S_(E) 235 may be estimated using themeasured signal S_(T) 236 from each pixel of the reference image frameand the difference in time between the end of exposure of a high-doseradiographic image and the frame time of the corrected image frame. Theestimated excess signal S_(E) 235 is then subtracted from the measuredsignal S_(T) of the corrected image frame to produce the true imagesignal S_(S) 239.

In one embodiment, the excess signal S_(E) 235 may be estimated using apower function (described below). In another embodiment, the excesssignal S_(E) 235 may be estimated using a look-up table (describedbelow). First, the method selects a frame rate, step 800. In step 810, anon-saturated, non-exposed image frame of the measured signal S_(T) 236is selected as a reference image frame. In step 820, the methoddetermines the difference in time between the frame time of the selectedreference image frame and the end of exposure time of the high-doseradiographic image. This difference in time may be determined using theframe rate. In another embodiment, time may be represented as framenumbers. In step 830, the excess signal S_(E) 235 of an image frame isestimated using the measured signal S_(T) 236 of the reference imageframe and the difference in time between the end of exposure time andthe frame time of the corrected image frame. The method in step 840subtracts the estimated excess signal S_(E) 235 of an image frame fromthe measured signal S_(T) 236 of the corrected image frame to producethe true image signal S_(S) 239. It should be noted that this method maybe repeated for all pixels of an image frame. The true image signalS_(S) 239 of each pixel of a frame provides a corrected image framewithout significant image errors and artifacts that may appear in theimage frame as “ghost” images from radiation incidents during one ormore prior frames.

FIG. 9 is a flow diagram illustrating one embodiment of a method ofestimating the excess signal S_(E) 235 in a pixel of a frame generatedby the imager sensor array 16 using two reference image frames, andcompensating for the excess signal S_(E) 235 in the pixel of a capturedframe. Each pixel of the first and second reference image frames has thecorresponding measured signals S_(T) 236. The excess signal S_(E) 235may be estimated using the measured signal S_(T) 236 of each pixel ofthe first reference image frame, the measure signal S_(T) 236 of eachpixel of the second reference image frame, the difference in timebetween the first frame time of the first reference image frame and thesecond frame time of the second reference image frame and the differencein time between the frame time of the first or second reference imageframe and the frame time of the captured image frame to be corrected.The estimated excess signal S_(E) 235 is then subtracted from themeasured signal S_(T) 236 of the corrected image frame to produce thetrue image signal S_(S) 239. The sources of excess signal S_(E) 235 maybe contributions from, for examples, leakage currents, dark/offsetcurrents, and lag currents from the capacitor 28, and/or from thephotoconductor 26, of the imager sensor array 16. It should be notedthat the excess charge Q_(E) 35 remaining from a radiographic image maycreate a “ghost” image in the subsequent fluoroscopic images. Estimatingand compensating for the signal S_(E) 235 representative of the excesscharge Q_(E) 35, reduces the residual “ghost” images presented byprevious frames.

In one embodiment, the excess signal S_(E) 235 may be estimated using apower function (described below). In one embodiment, the excess signalS_(E) 235 may be estimated using a look-up table (described below).First, the method selects a frame rate, step 900. In step 910, twonon-saturated, non-exposed image frames are selected as first and secondreference image frames. In step 920, the method determines thedifference in time between the first frame time of the first referenceimage frame and the second frame time of the second reference imageframe. This difference in time may be determined using the frame rate.In another embodiment, time may be represented as frame numbers. In step930, the excess signal S_(E) 235 of an image frame is estimated usingthe at least one of the measured signal S_(T) 236 of the first andsecond reference image frames and the difference in time between thefirst and/or second frame times to the selected frame for compensation.The method in step 940 subtracts the estimated excess signal S_(E) 235of an image frame from the measured signal S_(T) 236 of the image frameto produce the true image signal S_(S) 239. It should be noted that thismethod may be repeated for all pixels of an image frame. The true imagesignal S_(S) 239 of each pixel of a frame creates a corrected imageframe without significant image errors and artifacts that may appear inthe image frame as “ghost images” from radiation incidents during one ormore prior frames.

FIGS. 10A and 10B are exemplary fluoroscopic image frames illustratingcompensation for excess signal S_(E) 235 in an image F 1000 to producethe true image F 1010. FIGS. 10A and 10B contain the same fluoroscopicframe acquired shortly after radiographic exposure, uncompensated imageframe F 1000 and compensated image frame F 1010. For the radiographicexposure, 20 cm of acrylic were placed at an angle on the imager sensorarray 16. Approximately 3 seconds after the radiographic exposure theacrylic block was moved such that it became aligned to the horizontalorientation of the imager sensor array 16 and the fluoroscopicacquisition was started. Uncompensated frame F 1000 was acquiredapproximately 13 seconds after the radiographic exposure. The brighttriangle shaped areas 1020 in the upper left hand corner and lower righthand corner in FIG. 10A are due to signal contribution of theradiographic “ghost.” The compensated frame F 1010 of FIG. 10B uses thesame window and level as used for FIG. 10A. The triangular shaped areas1030 of FIG. 10B are significantly less visible than the triangle shapedareas 1020 of FIG. 10A.

FIGS. 11A and 11B are exemplary fluoroscopic image frames illustratingcompensation for signal S_(E) 235 in an image G 1100 to produce the trueimage G 1110 of a pelvis phantom. FIGS. 11A and 11B contain the samefluoroscopic frame acquired shortly after radiographic exposure,uncompensated image frame G 1100 and compensated image frame G 1110. Theuncompensated frame G 1100 displayed in FIG. 11A shows an area 1130where the signal contribution from the radiographic “ghost” introduces avisible image artifact 1140. FIG. 11B illustrates a compensated imageframe G 1110 after estimating and compensating for the signal S_(E) 235in the uncompensated image frame G 1100. The compensation of signalS_(E) 235 reduces the artifact 1140 of the area 1130 of FIG. 11A.

FIG. 12 illustrates one example of a graph 1200 showing the measuredsignal level as a function of time of imaging system 2. The measuredsignal level in time has two stages. The first stage is the measuredsignals during the exposure time T_(exp) 1220 of a non-saturated exposedimage 1211 of the imaging system 2. The second stage of the measuredsignal levels shows the non-saturated excess signal 1212 after the endof exposure time T_(exp) 1220. The measured signal S_(T) 236 is obtainedA/D conversion of the measured charge at node 34 as previously discussedin relation to FIGS. 2A-2C.

The measured signal S_(T) 236 of the high-dose non-saturated exposedimage 1211 of FIG. 12 is represented as being a constant line at acharge level L_(ref) 1251. In another embodiment, the measured high-dosenon-saturated exposed image 1211 may be illustrated as a time-varyingfunction. The measured charge of the high-dose non-saturated exposedimage 1211 is measured at charge level L_(ref) 1251 below the signalsaturation level L_(SAT) 1231. The non saturated excess signal 1212 isthe amount of excess signal after the end of exposure time T_(exp) 1220.Sources of the excess signal 1212 may be, for examples, leakagecurrents, dark/offset currents, and lag contribution currents from thecapacitor 28, and/or from the photoconductor 26, and/or from the switch32, of the imager sensor array 16. If not removed, the contribution dueto the excess signal 1212 introduces “ghost” images in the subsequentimages.

Graph 1200 illustrates the non-saturated excess signal 1212 having anon-linear decay response after the end of exposure time T_(exp) 1220 ofa high dose non-saturated exposed image 1211. An exemplary non-saturatedexcess signal 1212 automatically begins to decay because the measuredhigh-dose non-saturated exposed image 1211 is at a non-saturated signallevel L_(ref) 1251 (L_(ref) 1251 is less than current saturation levelL_(SAT) 1231). The method described with respect to FIG. 8 uses thenon-saturated excess signal 1212 to estimate the excess signal S_(E) 235of subsequent frames. As described in FIG. 8, step 810, a non-saturatedreference image frame is selected. The reference image frame F_(ref1)1240 is illustrated in FIG. 12. The method uses the measurednon-saturated charge level L_(D1) 1241 and the difference in time t_(D1)1260, determined in step 820, to estimate the excess signal, step 830.The method subtracts the estimated excess signal S_(E) 235, step 840, tocompensate the measured signal S_(T) 236 to produce a true image S_(S)239 output from imaging system 2. The difference in time t_(D1) 1260 isdetermined by subtracting the frame time T_(ref1) 1230 of the referenceimage frame F_(ref1) 1240 of the measured non-saturated excess signal1212, from the end of exposure time T_(exp) 1220, step 820. In oneembodiment, the excess signal S_(E) 235 may be estimated using thedifference in time t_(D1) 1260 and the measured L_(D1) 1241 of referenceimage frame F_(ref1) 1240 in a function of integration time as describedpreviously in relation to FIG. 7. In another embodiment, the excesssignal S_(E) 235 may be estimated using the difference in time t_(D1)1260 and the measured L_(D1) 1241 of reference image frame F_(ref1) 1240in a power function. In another embodiment, the excess signal S_(E) 235may be estimated using the difference in time t_(D1) 1260 and themeasured L_(D1) 1241 of reference image frame F_(ref1) 1240 in a look-uptable. In another embodiment, the excess signal S_(E) 235 may bedetermined using a power function and a look up table. In anotherembodiment, the difference in time t_(D1) 1260, the end of exposure timeT_(exp) 1220, and the frame time T_(ref1) 1230 of reference image frameF_(ref1) 1240, may be in terms of frame numbers. The frame numbers maybe computed using the frame rate as known to one of ordinary skill inthe art.

FIG. 13 illustrates one example of a graph 1300 showing the measuredsignal levels as a function of time of imaging system 2. The measuredsignal S_(T) 236 in time has three stages. The first stage is themeasured signal up to the end of the exposure time T_(exp) 1320 of ahigh-dose saturated exposed image 1311. The second stage of the measuredsignal S_(T) 236 shows the saturated excess signal 1312 after the end ofexposure time T_(exp) 1320. The third stage of the measured signal S_(T)236 shows the non-saturated excess signal 1313 after the end ofsaturation time T_(SAT) 1321. The measured signal S_(T) 236 is obtainedin the same manner as described in relation to FIG. 12.

The measured signal S_(T) 236 of the high-dose saturated exposed image1311 of FIG. 13 is represented as being a constant line because themeasured signal S_(T) 236 is saturated at the signal saturation levelL_(SAT) 1331. The measured saturated excess signal 1312 is alsosaturated at the signal saturation level L_(SAT) 1331 and is representedas a constant line until the end of saturation time T_(SAT) 1321.

Graph 1300 illustrates the non-saturated excess signal 1313 having anon-linear decay response after the end of exposure time T_(exp) 1320 ofa high dose non-saturated exposed image 1311. The method described withrespect to FIG. 8 uses the measured non-saturated signal S_(T) toestimate the excess signal S_(E) 235 of subsequent frames. As describedin FIG. 8, step 810, a non-saturated reference image frame is selected.The reference image frame signal F_(ref1) 1340 is illustrated in FIG.13. The method uses the measured non-saturated signal level L_(D1) 1361,the difference in time t_(D1) 1360 and the difference in time betweenthe end of the exposure T_(exp) and the time of the frame beingcorrected (compensated), as determined in step 820, to estimate theexcess signal S_(E) 235, step 830. The method subtracts the estimatedexcess signal S_(E) 235, step 840, to compensate the measurednon-saturated signal 1313 to produce a true image signal S_(S) 239 atthe output of imaging system 2. The difference in time t_(D1) 1360 isdetermined by subtracting the frame time T_(ref1) 1330 of the referenceimage frame signal F_(ref1) 1340 of the measured non-saturated excesssignal 1313, from the end of exposure time T_(exp) 1320, step 820. Inone embodiment, the excess signal S_(E) 235 may be estimated using thedifference in time t_(D1) 1360 and the measured signal level L_(D1) 1361of reference image frame signal F_(ref1) 1340 in a function ofintegration time as described previously in relation to FIG. 7. Inanother embodiment, the excess signal S_(E) 235 may be estimated usingthe difference in time t_(D3) 1360 and the measured signal level L_(D1)1361 of reference image frame signal F_(ref1) 1340 in a power function.In another embodiment, the excess signal S_(E) 235 may be estimatedusing the difference in time t_(D3) 1360 and the measured signal levelL_(D1) 1361 of reference image frame F_(ref1) 1340 in a look-up table.In another embodiment, the excess signal S_(E) 235 may be determinedusing a power function and a look up table. In another embodiment, thedifference in time t_(D3) 1360, the end of exposure time T_(exp) 1320,the end of saturation time T_(SAT) 1321, and the frame time T_(ref1)1330 of reference image frame F_(ref1) 1340, and the difference in timebetween the end of exposure time T_(exp) 1320 and the time of the imageframe to be corrected, may be in terms of frame numbers. The framenumbers may be computed using the frame rate as known to one of ordinaryskill in the art.

FIG. 14 illustrates one example of a graph 1400 showing the measuredsignal level as a function of time. The measured signal S_(T) 236 intime has three stages. The first stage is the measured signal S_(T) 236up to the end of the exposure time T_(exp) 1420 of a high-dose saturatedexposed image 1410. The second stage of the measured signal S_(T) 236shows the saturated excess signal S_(E) 1412 after the end of exposuretime T_(exp) 1420. The third stage of the measured signal S_(T) 236shows the non-saturated excess signal S_(E) 1413 after the end ofsaturation time T_(SAT) 1421. The measured signal S_(T) 236 may beobtained in the same manner as described in relation to FIG. 12. Themeasured charge of the high-dose saturated exposed image 1410 of FIG. 14is represented as being a constant line because the signal is saturatedat the signal saturation level L_(SAT) 1431. The measured saturatedexcess signal 1412 is also saturated at signal saturation level L_(SAT)1431 and is represented as a constant line until the end of saturationtime T_(SAT) 1421.

Graph 1400 illustrates the measured non-saturated excess signal 1413having a non-linear decay response after the end of saturation timeT_(SAT) 1421 of a high dose non-saturated exposed image 1411. The methoddescribed with respect to FIG. 9 uses the measured non-saturated excesssignal 1413 to estimate the excess signal S_(E) 235 of subsequentframes. As described in FIG. 9, step 910, two non-saturated referenceimage frames are selected. The first reference image frame F_(ref1) 1440and the second reference image frame F_(ref2) 1441 are illustrated inFIG. 14. The method uses the measured non-saturated signal levels L_(D1)1481 and L_(D2) 1491, the difference in time t_(D3) 1460 and thedifference in time between the first or the second reference frame timeand the time of the image frame to be corrected, determined in step 920,to estimate the excess signal S_(E) 235, step 930. The method subtractsthe estimated signal S_(E) 235, step 940, to compensate the measuredexcess signal 1413 to produce a true image charge S_(S) 239. Thedifference in time t_(D3) 1460 is determined by subtracting the firstframe time T_(ref1) 1430 of the reference image frame F_(ref1) 1440 fromthe second frame time T_(ref2) 1431 of the reference image frameF_(ref2) 1441 of the measured non-saturated excess signal 1413, step920. In one embodiment, the excess signal S_(E) 235 may be estimatedusing the difference in time t_(D3) 1460, the measured signal levelL_(D1) 1481 and L_(D2) 1491 of reference image frames F_(ref1) 1440 andF_(ref2) 1441 and the difference in time between the first or the secondreference frame time and the time of the image frame to be corrected ina function of integration time as described previously in relation toFIG. 7. In another embodiment, the excess signal S_(E) 235 may beestimated using the difference in time t_(D3) 1460, the measure signallevel L_(D1) 1481 and L_(D2) 1491 of reference image frames F_(ref1)1440 and F_(ref2) 1441 and the difference in time between the first orthe second reference frame time and the time of the image frame to becorrected in a power function. In another embodiment, the excess signalS_(E) 235 may be estimated using the difference in time t_(D3) 1460, themeasure signal level L_(D1) 1481 and L_(D2) 1491 of reference imageframes F_(ref1) 1440 and F_(ref2) 1441 and the difference in timebetween the first or the second reference frame time and the time of theimage frame to be corrected in a look-up table. In another embodiment,the excess signal S_(E) 235 may be estimated using the difference intime t_(D3) 1460, the measured signal level L_(D1) 1481 and L_(D2) 1491of reference image frames F_(ref1) 1440 and F_(ref2) 1441 and thedifference in time between the first or the second reference frame timeand the time of the image frame to be corrected in a recursive function.

In another embodiment, the difference in time t_(D3) 1460, the end ofexposure time T_(exp) 1420, the difference in time t_(D1) 1451, thedifference in time t_(D2) 1452, the end of saturation time T_(SAT) 1421,the first frame time T_(ref1) 1430 of the first reference image frameF_(ref1) 1440, the second frame time T_(ref2) 1431 of the secondreference image frame F_(ref2) 1441, and the difference in time betweenthe first or second reference frame time and the time of the image frameto be corrected, may be in terms of frame numbers. The frame numbers maybe computed using the frame rate as known to one of ordinary skill inthe art.

In one embodiment, a power function may be used in estimating the excesssignal S_(E) 235, as described in relation to FIGS. 8, 9, 12, 13, and14. The following description and equations are used as one method ofestimating the excess signal S_(E) 235 using a power function. The powerfunction estimates the excess signal S_(E) 235 of the measured signalS_(T) 236. After compensating for the excess signal S_(E) 235 of themeasured signal S_(T) 236, using the power function, the excess signalS_(E) 235 may be subtracted from the measured signal S_(T) 236 toproduce a corrected true image signal S_(S) 239 without “ghost” imagesfrom previous radiographic image frames. It should be noted that thepower function estimation of the excess signal S_(E) 235 may be done foreach pixel of a frame. The compensation of the excess signal S_(E) 235may also be done for each pixel of a frame to create true image signalS_(S) 239.

One example of the power function approximation is shown in thefollowing equations.

$\begin{matrix}{{S_{E}(t)} \cong {{S_{E}\left( t_{o} \right)} \cdot t^{- \alpha}}} & (5) \\{{S_{E}({nT})} \cong {{S_{E}\left( t_{o} \right)} \cdot ({nT})^{- \alpha}}} & (6) \\{T = \frac{1}{FrameRate}} & (7)\end{matrix}$

Equation (5) approximates the excess signals S_(E) 1212, 1313, and 1413shown in FIGS. 12, 13, and 14, respectively. S_(E)(t) represents theestimated excess signals 1212, 1313, and 1413. Exponent α can be assumedto be constant for a wide range of radiographic exposures. Thecontinuous time variable t is the time after the end of exposure T_(exp)1220, 1320, and 1420. S_(E)(t₀) represents a lag reference constant ofthe excess signals 1212, 1313, or 1413. Constant S_(E)(t₀) is unique foreach radiographic exposure. In another embodiment, the continuous timevariable t of equation (5) may be replaced with discrete frame time nT,equation (6). T is the reciprocal of the frame rate of the imager sensorarray 16, equation (7). The variable n is a positive integer such thatdiscrete frame time nT is greater than end of exposure time T_(exp)1220, 1320, and 1420. Equation (6) illustrates this substitution andshows the discrete nature of the imager sensor array 16.S _(Ecomp)(t)=S _(Emeas)(t)−S _(E)(t)  (8)S _(Ecomp)(t)=S _(Emeas)(t)−S _(E)(t _(o))·(t)^(−α)  (9)

Equation (8) illustrates how the excess signal S_(E) of image F issubtracted from the measured signal S_(T) 36 of Frame F to obtain thecompensated signals S_(S)(t). S_(S)(t) represents the charge of frame Fafter compensation as a function of time. S_(T)(t) represents themeasured charge of frame F before compensation at a particular point intime after T_(exp) 1220, 1320, and 1420. S_(E)(t) represents, asdescribed in relation to (5), the approximation of the excess signals1212, 1313, and 1413 as a function of time, as shown in FIGS. 12, 13,and 14, respectively. Combining the two equations (5) and (8), resultsin equation (9).S _(Ecomp)(nT)=S _(Emeas)(nT)−S _(E)(nT)  (10)S _(Ecomp)(nT)=S _(Emeas)(nT)−S _(E)(t _(o))·(nT)^(−α)  (11)

Equation (10) illustrates how the excess signal S_(E) of image F issubtracted from the measured signal S_(T) 26 of Frame F to compensatefor that excess signal S_(E) 235 as a function of frame number.S_(S)(nT) represents the charge of frame F after compensation as afunction of frame number. S_(T) (nT) represents the measured signalS_(T) 236 of frame F before compensation for a particular frame.S_(E)(nT) represents, as described in relation to equation (6), theapproximation of the excess signals 1212, 1313, and 1413 as a functionof frame number. Combining the equations (6) and (10) results inequation (11).S _(E)(t _(o))(t _(D1))=L _(D1) ·t _(D1) ^(α)  (12)t _(D1) =T _(ref1) −T _(exp)  (13)S _(E)(t)=S _(E)(t)−(L _(D1) ·t _(D1) ^(α))·(t)^(−α)  (14)

Equation (12) illustrates how the lag reference constant S_(E)(t₀) isderived if the time reference t_(D1) is known. Time reference t_(D1)represents the difference in time of the end of the exposure T_(exp) andthe time of reference of the first reference image frame acquiredT_(ref1), as shown in equation (13). Examples of t_(D1) are shown inFIGS. 12, and 13, as the difference in time t_(D1) 1260, and thedifference in time t_(D1) 1360, respectively. Signal level L_(D1) 1241and signal level L_(D1) 1361 of FIGS. 12, and 13, represent the measuredsignal of the acquired reference image frames F_(ref1) 1240, andF_(ref1) 1340, respectively. Combining equations (9) and (12) results inequation (14). It should be noted that the variable t of equations (12),(13), and (14) may be in terms of a particular frame number in discreteframe time nT. The particular frame number in discrete frame time nT, isdetermined by n, the positive integer frame number, and the reciprocalof the frame rate, T (see equation (7)).

$\begin{matrix}{t_{D\; 1} \approx \frac{t_{D\; 3}}{\left( {\left( \frac{L_{D\; 1}}{L_{D\; 2}} \right)^{\frac{1}{\alpha}} - 1} \right)}} & (15) \\{t_{D\; 3} = {t_{{ref}\; 2} - t_{{ref}\; 1}}} & (16) \\{L_{D{({k + 1})}} = {L_{D\; 1} \cdot \left( {1 + {k \cdot \left( {\left( \frac{L_{D\; 1}}{L_{D\; 2}} \right)^{\frac{1}{\alpha}} - 1} \right)}} \right)^{- \alpha}}} & (17) \\{L_{D{({k + 1})}} = {L_{D\; 1} \cdot \left( \frac{1}{\left( {1 + {k \cdot \left( \frac{L_{D\; 1}}{L_{D\; 2}} \right)} - 1} \right)} \right)}} & (18)\end{matrix}$

Equation (15) illustrates how to approximate the time t_(D1) used inequation (12) to calculate the lag reference constant S_(E)(t₀), if thetime elapsed between the end of the radiographic exposure T_(exp) 1420and the time references T_(ref1) 1430 and T_(ref2) 1431 of FIG. 14 areunknown. The difference in time t_(D3) 1460 is the difference in timebetween the first frame time T_(ref1) 1430 of the first reference imageframe 1440 and the second frame time T_(ref2) 1431 of the secondreference image frame 1441, equation (15). Signal level L_(D1)represents the measured charge of the first reference image frameF_(ref1) 1440. Signal level L_(D2) represents the measured charge of thesecond reference image frame F_(ref2) 1490. If difference in time t_(D3)1460 is set equal to time T of equation (15), which is the reciprocal ofthe frame rate (equation (7)), then equations (12) and (14) may becombined to become equation (17). The variable k of equation (17)represents a positive integer number starting at one. Signal levelL_(D(k+1)) of equation (17) represents the estimated excess signal S_(E)235 for the next frame. Measured values for the constant α of equation(17) range from 1.05 to 1.08 in imager sensor array 16. In oneembodiment, in order to simplify hardware implementation the constant αmay be set to equal 1.0. The simplified equation (17), substituting theconstant α with the number 1.0, is shown in equation (18).

FIG. 15 illustrates one example of a look-up table used to index thepre-calculated estimated excess signals using the measured signals at agiven time. The selected excess signal may then be compensated for inthe measured signals to produce the true signal of the image. Thelook-up table is used in one embodiment, to index a pre-calculatedexcess signal to estimate the excess signal S_(E) as a function of time.In another embodiment, the look-up table is used to index apre-calculated excess signal to estimate the excess signal S_(E) as afunction of frame number. The frame number and the measured charges ofthe reference image frame are used to index the correspondingpre-calculated excess charge. The indexed pre-calculated excess signalmay be subtracted from the measured signal of the image to produce thetrue image signal S_(S). It should be noted that pre-calculated excesssignal may be indexed for each pixel. The true image signal S_(S) ofeach pixel creates a true image frame signal.

In one embodiment, the look up table 1500 may use frame numbers 1510 andthe measured reference image frame signals 1520 to index pre-calculatedexcess signals S_(PRE) 1530. The frame numbers 1510 may correspond tothe frame times T_(ref1) 1230, T_(ref1) 1330, T_(ref1) 1430, andT_(ref1) 1431 of FIGS. 12, 13, and 14. The measured reference imageframe signals 1520 may correspond to the measured signal levels L_(D1)1241, L_(D1) 1361, L_(D1) 1481, and L_(D2) 1491 of the selectedreference image frames 1240, 1340, 1440, and 1441, respectively.Pre-calculated excess signals S_(PRE) 1530, in one embodiment, may bepre-calculated estimations of the excess signal S_(E) 235 using theintegration function of FIG. 4. In another embodiment, thepre-calculated excess signals S_(PRE) 1530 may be pre-calculated usingthe power function. In another embodiment, the pre-calculated excesssignals S_(PRE) 1530 may be pre-calculated by testing the behavior ofthe sensor array through a non-linear range of operation. In anotherembodiment, the pre-calculated excess signals S_(PRE) 1530 may bedetermined by simulating the behavior of a sensor array through anon-linear range of operation. In another embodiment, the pre-calculatedexcess signals S_(PRE) 1530 may be determined by theorizing the behaviorof sensor array through a non-linear range of operation. Thepre-calculated excess signals S_(PRE) 1530 may then be subtracted fromthe measured signal S_(T) 236 of an image frame to compensate for theexcess signal S_(E) 235 present in the measured signal S_(T) 236.

In another embodiment, a recursive function may be used in estimatingthe excess signal S_(E) 235. The following description and equations areused as one method of estimating the excess signal S_(E) 235 using arecursive function. The recursive function estimates the excess signalS_(E) 235 of a frame (N) to be corrected using the calculated excesssignal S_(E) 235 of the previous frame (N−1) and a coefficient α, whichis recalculated for every consecutive frame to be corrected. Thecoefficient α for the first frame to be corrected is determined usingthe measured signal S_(T) 236 of the two previous consecutive referenceframes. After estimating the excess signal S_(E) 235 using the recursivefunction, the excess signal S_(E) 235 may be subtracted from themeasured signal S_(T) 236 of the frame to produce a corrected true imagesignal without any “ghost” images that may be introduced by previousradiographic image frames.S _(EN) =S _(EN−1) ·αN  (19)α_(N)=α_(N−1) +Kp·(1−α_(N−1))²  (20)

One example of the recursive function approximation is shown inequations (19) and (20). The recursive function in equation (19)calculates the excess signal S_(EN) of the lag frame N by multiplyingthe excess signal S_(EN−1) of the previous lag frame N−1 by acoefficient α_(N). Coefficient α_(N) is calculated in equation (20)using a constant Kp and the coefficient of the previous frame α_(N−1).Constant Kp is dependent on the attributes of the imager sensor array 16and, in one embodiment, may be in the range of 0.5 to 1.1. Coefficientα_(N) is calculated for every new frame.

FIG. 16A illustrates one example of a graph showing the remaining excesssignal S_(E) 235 of an image after compensation using three differentestimation functions as a function of frame number. The error signalcount 1610 resulting from the estimation methods 1640, 1650, and 1660,illustrated in FIGS. 16A and 16B, are examples of the estimations madein the steps 720, 830, and 930 of the methods described in FIGS. 7, 8,and 9, respectively. The graph 1600 a includes the error signal count1610 of the actual measured signal S_(T) 236 of an image 1630 withoutcompensation for the excess signal S_(E) 235. The graph 1600 a alsoincludes the error signal count 1610 of the remaining excess signalS_(E) 235 after compensation using three different estimation methods asa function of frame number 1620. The three estimation methods are aconstant decay function 1640, a power function 1650, and a recursivefunction 1660.

FIG. 16B illustrates the same remaining excess signal S_(E) 235 for twoof the estimation methods as a function of frame number at a smallerscale than FIG. 16A. Graph 1600 b illustrates the error signal counts1610 of the power function 1650, and the recursive function 1660. Theactual excess signal S_(E) without compensation 1630, and the constantdecay function 1640 are not shown in graph 1600 b because they areoutside the scale of the graph. In mixed radiographic/fluoroscopyapplications, lower dose fluoroscopy images are acquired shortly after ahigher dose radiographic exposure. The remaining excess signal from theradiographic exposure may appear as a “ghost” image in the fluoroscopicimages. If the error count of the remaining excess signal S_(E) 235after compensation can be lowered the “ghost” appearing in the imagescan be corrected. The error counts illustrated in FIG. 16B correspond toan x-ray dose of approx. 0.5 uR/frame, which is about half of theminimum dose recommended for the fluoroscopy mode of imager sensor array16. An estimation of excess signal method that permits the error signalcount 1610 to be below 400 error counts after compensation may reduce orcorrect any “ghost” images that may be present in subsequentfluoroscopic images that are introduced from previous radiographicexposures. Compensation using the estimation method of constant decay1640 of FIG. 16A may not sufficiently compensate for the excess signalbecause the levels of the error signal count 1610 have a maximumabsolute magnitude above 400-error count. The remaining excess signalafter compensation using the power function 1650 and the recursivefunction 1660 have maximum absolute magnitudes lower than 10 counts. Thepower function 1650 and the recursive function 1660 having an errorsignal count lower than 10 may sufficiently reduce or correct any“ghost” images that may be present due to excess signal S_(E) 235.

The particular methods of the invention have been described in terms ofcomputer software with reference to a series of flowcharts. The methodsto be performed by computing device 4 constitute computer programs madeup of computer-executable instructions illustrated as blocks (acts).Describing the methods by reference to a flowchart enables one skilledin the art to develop such programs including such instructions to carryout the methods on suitably configured computers (the processing unit ofthe computer executing the instructions from computer-readable media).The computer-executable instructions may be written in a computerprogramming language or may be embodied in programmable or discretelogic. If written in a programming language conforming to a recognizedstandard, such instructions can be executed on a variety of hardwareplatforms and for interface to a variety of operating systems. Inaddition, the present invention is not described with reference to anyparticular programming language. It will be appreciated that a varietyof programming languages may be used to implement the teachings of theinvention as described herein. Furthermore, it is common in the art tospeak of software, in one form or another (e.g., program, procedure,process, application, module, logic . . . ), as taking an action orcausing a result. Such expressions are merely a shorthand way of sayingthat execution of the software by a computer causes the processor of thecomputer to perform an action or a produce a result. It will beappreciated that more or fewer processes may be incorporated into themethods as described above without departing from the scope of theinvention, and that no particular order is implied by the arrangement ofblocks shown and described herein.

In the foregoing specification, the invention is described withreference to specific embodiments thereof. It will, however, be evidentthat various modifications and changes may be made thereto withoutdeparting from the broader spirit and scope of the invention as setforth in the appended claims. The specification and drawings are,accordingly, to be regarded in an illustrative rather than a restrictivesense.

1. A method, comprising: estimating an excess signal based on acombination of a first and a second non-linear decay response model of ameasured signal of at least one image frame of an imaging system; andcompensating for the excess signal in the at least one image frame usingthe estimated excess signal; wherein the model comprises arepresentation of a measured signal of the at least one image frame. 2.The method of claim 1, wherein model comprises a non-linear time variantdecay response model.
 3. A method, comprising: estimating an excesssignal based on a combination of a non-linear decay response model and alinear decay response model of a measured signal of at least one imageframe of an imaging system; and compensating for the excess signal inthe at least one image frame using the estimated excess signal; whereinthe mode comprises a representation of a measured signal of the at leastone image frame.
 4. The method of claim 3, wherein model comprises anon-linear time variant decay response model.